1. Friction Inclines Problem-Solving Approaches

2. The origin of friction is electric forces between atoms of materials in contact. We will be concerned with two kinds of frictional forces: forces between stationary objects and forces between moving objects. Frictional forces result from surfaces in contact. Frictional forces oppose the sliding of surfaces in contact. Static friction forces point opposite to the direction of motion an object would move over a surface if no friction were present. Figure out which way an object would move without friction present. Then F static is aimed the opposite direction. 4.8 Applications Involving Friction, Inclines

3. If the object is sliding down the plane, the frictional force is “kinetic” and directed up the plane. If the object is stationary, then the component of its weight down the plane “wants” to pull it down. The frictional force is “static” and is directed up the plane. FkFk FsFs If some object is pushing (or pulling) the object up the plane, the frictional force is “kinetic” and is directed down the plane. FkFk P v v

4. If some force is just about to push (or pull) the object up the plane, the frictional force is “static” and is directed down the plane. FsFs P Of course, friction acts between when a surface is horizontal or vertical, as well as tilted. P v FkFk

5. We model the magnitudes of frictional forces using these two official starting equations: Experimentally, the magnitude of frictional forces is observed to be proportional to the normal force between objects, and the direction is opposite to the motion, or the impending motion. Here are a couple of toys to play with: http://physics.bu.edu/~duffy/java/SecondLaw2.html http://physics.bu.edu/~duffy/java/SecondLaw.html Usually, μ s > μ k. What does this have to do with antilock brakes?

6. Static friction forces start out zero and increase up to a maximum. If I try to pull a lead brick across a rough surface using very little “pull,” the friction force will be small, but sufficient to overcome my “pull.” The friction force will increase as I increase the “pull.” Eventually, when my “pull” exceeds the maximum static friction force, the brick starts accelerating.

7. In the case of both static and kinetic friction forces, the friction force opposes motion of one surface across the other, so it is directed parallel to the surfaces. The friction force is not necessarily directed opposite to an applied force, as in the diagram to the right. P v FkFk HereHere are some notes from another class. They represent a different way of presenting the above material. I am going to paste them into this lecture, so you are about to get a 2 nd perspective on what I just covered.

8. Where would we be without friction? —slip-sliding away Friction is not a “separate” kind of force—it is a result of electromagnetic forces between microscopic objects. Friction forces oppose actual motion (kinetic friction) or motion that would take place if no friction were present (static friction).

9. Friction is a force, so it is a vector. Friction forces occur at contact points between surfaces and are always directed parallel to the (local) surface. Kinetic friction forces on a surface point in the direction parallel to the surface and opposite the velocity. Static friction force direction: figure out which way an object would move without friction. Then is aimed in the opposite direction.

16. This is what we’ve been doing all along! There is no new material in this section. 4.9 Problem Solving—A General Approach Work friction examples: (a) what is the force of friction on a block at rest on an inclined plane; (b) what is the maximum angle for block to remain at rest on an inclined plane.